diff --git a/Doc/library/random.rst b/Doc/library/random.rst
index 1bd1856..933da3f 100644
--- a/Doc/library/random.rst
+++ b/Doc/library/random.rst
@@ -165,8 +165,9 @@
 
    The *weights* or *cum_weights* can use any numeric type that interoperates
    with the :class:`float` values returned by :func:`random` (that includes
-   integers, floats, and fractions but excludes decimals).  Weights are
-   assumed to be non-negative.
+   integers, floats, and fractions but excludes decimals).  Behavior is
+   undefined if any weight is negative.  A :exc:`ValueError` is raised if all
+   weights are zero.
 
    For a given seed, the :func:`choices` function with equal weighting
    typically produces a different sequence than repeated calls to
@@ -177,6 +178,9 @@
 
    .. versionadded:: 3.6
 
+   .. versionchanged:: 3.9
+      Raises a :exc:`ValueError` if all weights are zero.
+
 
 .. function:: shuffle(x[, random])
 
diff --git a/Lib/random.py b/Lib/random.py
index be4401c..e24737d 100644
--- a/Lib/random.py
+++ b/Lib/random.py
@@ -413,8 +413,10 @@
             raise TypeError('Cannot specify both weights and cumulative weights')
         if len(cum_weights) != n:
             raise ValueError('The number of weights does not match the population')
-        bisect = _bisect
         total = cum_weights[-1] + 0.0   # convert to float
+        if total <= 0.0:
+            raise ValueError('Total of weights must be greater than zero')
+        bisect = _bisect
         hi = n - 1
         return [population[bisect(cum_weights, random() * total, 0, hi)]
                 for i in _repeat(None, k)]
diff --git a/Lib/test/test_random.py b/Lib/test/test_random.py
index f59c565..2c8c8e8 100644
--- a/Lib/test/test_random.py
+++ b/Lib/test/test_random.py
@@ -241,6 +241,11 @@
         choices = self.gen.choices
         choices(population=[1, 2], weights=[1e-323, 1e-323], k=5000)
 
+    def test_choices_with_all_zero_weights(self):
+        # See issue #38881
+        with self.assertRaises(ValueError):
+            self.gen.choices('AB', [0.0, 0.0])
+
     def test_gauss(self):
         # Ensure that the seed() method initializes all the hidden state.  In
         # particular, through 2.2.1 it failed to reset a piece of state used
diff --git a/Misc/NEWS.d/next/Library/2019-11-22-20-03-46.bpo-38881.7HV1Q0.rst b/Misc/NEWS.d/next/Library/2019-11-22-20-03-46.bpo-38881.7HV1Q0.rst
new file mode 100644
index 0000000..9f4a27d
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-11-22-20-03-46.bpo-38881.7HV1Q0.rst
@@ -0,0 +1 @@
+random.choices() now raises a ValueError when all the weights are zero.